1. Field of the Invention
The present invention relates to a method and an apparatus for analyzing contaminative element concentrations, and more specifically to a method and an apparatus for measuring contaminative element concentrations on a semiconductor substrate, for instance with the use of an energy dispersive type total refection X-ray fluorescence analysis.
2. Description of the Background Art
Conventionally, as a non-destructive contaminative element concentration analyzing apparatus, there is so far known a total reflection X-ray fluorescence analysis (See "Inspection, Analysis and Measurement Technology Required 16M/64M Integration or After", by Ayako SIMAZAKI, Kunihiro MIYAZAKI; NIKKEI MICRODEVICE, No. 86, pages 148, 154, 156 and 158, August, 1992). Furthermore, as a contaminative element concentration analyzing apparatus based upon total reflection X-ray fluorescence analysis, an energy or wavelength dispersive type apparatus is known. Since the contaminative element concentrations can be analyzed nondestructively with the use of the contaminative element concentration analyzer based upon the total reflection X-ray fluorescence analysis, it has become possible to manage the contamination of silicon wafer during the semiconductor manufacturing process, and thereby the contamination of wafer can be reduced effectively.
FIG. 4 is a conceptual block diagram showing an example of the contaminative element concentration analyzer using the energy dispersive type total reflection X-ray fluorescence analysis.
In FIG. 4, a sample base 4 is mounted within a vacuum chamber 41, and a sample (e.g., silicon wafer) 43 is mounted on this sample base 2. an X-ray generated by a rotating pair-cathode type X-ray source 4 is converted to a monochromatic ray through a monochrometer 45, being passed through a slit 49, and then allowed to be incident upon the sample 43 at a small total-reflection angle. On the basis of this incident X-ray, a fluorescent X-ray can be generated from the surface of the sample 43. The generated fluorescent X-ray is detected by a detector (e.g., semiconductor detector), and converted into electric signals corresponding thereto. The fluorescent X-ray signals detected as described above are processed by a pulse processor 47 to obtain an observed waveform as shown in FIG. 5. In FIG. 5, the abscissa designates the energy of the detected fluorescent X-ray and the ordinate designates the signal intensity (relative intensity according to the number of photons incident upon the detector 46) of the detected fluorescent X-ray. FIG. 5 indicates that the observed waveform (graph) has a peak value for each element (silicon and other contaminative elements) contained in the silicon wafer 43. In addition, the integral intensity (which corresponds to an area of a peak waveform) of each peak is proportional to the concentration of the element.
On the other hand, an arithmetic processing circuit 48 stores information indicative of the relationship between the integral intensity of the fluorescent X-ray and the concentration for each contaminative element, which is referred to as "analytical curve". Therefore, the arithmetic processing circuit 48 first separates the peaks of the contaminative elements from the observed waveform (See FIG. 5) inputted by the pulse processor 47 for concentration detection, and then calculates the respective integral intensities of the separated peaks, and obtains the contaminative element concentrations on the basis of the integral intensities and the analytical curves.
A co-pending U.S. Patent Application Ser. No. 08/116,750 now U.S. Pat. No. 5,422,925 which is incorporated herein discloses a method of peak separation.
Here conventionally, the peaks of the contaminative elements have been separated as follows:
(1) First, the respective peaks are detected on the basis of the observed waveform (See FIG. 5). In this peak detection, the observed waveform is first processed for smoothing differentiation to obtain third-order differentiated waveform. After that, zero points are detected from the obtained three-degre differentiated waveform, and further the peaks are detected from these detected zero points under the conditions that the quadratic differential value is minimized and further the fluorescent X-ray intensity of the observed waveform exceeds a predetermined value.
(2) Furthermore, for each of the respective detected peaks, a tentative value such as a peak position, a peak height, a half width of half maximum (a deviation of a point on the distribution curve at a half value of the peak height from the average value), etc. are set.
(3) The respective peaks are processed for nonlinear optimization in accordance with a model function having the peak position, the peak height, and the half width of half maximum as parameters (by using the above-mentioned tentative values as initial values), and further such a peak position, a peak height and a half width of half maximum that a differential square sum between the model function and the observed waveform can be minimized are obtained, respectively. In accordance with the method as described above, it is possible to separate the respective required peaks of the contaminative elements from the observed waveform.
In the above-mentioned peak separating method of the conventional contaminative element concentration analyzing apparatus, however, there the observed waveform is distorted; that is, the waveform peak is split, there exists such drawbacks that a plurality of peaks are superposed upon each other. For instance, FIG. 6A shows an observed waveform of Fe and Ni (which corresponds to the energy range between 6.89 and 8.01 eV in FIG. 5)), and a1 denotes the peak waveform of K.alpha. of Ni and a2 denotes the peak waveform of K.beta. ray of Fe, respectively. In the case where there exist such peak splits, the peak a1 shown in FIG. 6A is discriminated as two peaks b1 and b1' superposed upon each other, and the peak a2 shown in FIG. 6A is discriminated as two peaks b2 and b2' superposed upon each other, as shown in FIG. 6B.
In the case of the conventional method, the fact that the waveform having peak splits is discriminated as two peak superposition is a normal discrimination result. However, in practice, since there exists no such peak superposition, this implies that the number of peaks is detected erroneously.
Further, where the waveform having peak splits is discriminated as a plurality of peaks superposed upon each other, since the respective peak heights or the respective half widths of half maximum of the detected peaks are inevitably produced erroneously, when the integral intensities of the peaks are calculated at the succeeding stage, an error occurs, so that the analysis results of the concentrations are not accurate.